Angelica is working with function machines. she has the two machines at shown at the right. she wants to put them in order so that the output of the first machine becomes the input of the second. her initial input is six.

Put the machine with the function y = x^2 - 6 first and then the machine with the function y = sqrt(x-5).

a) In this way, you obtain x = 6 => y = 6^2  - 6 = 36 - 6 = 30 as the output of the first machine and the input of the second machine.

Then the second machine will transform 30 to sqrt (30 - 5) = sqrt (25) = 5, which the the final output wanted.

b) To obtain a final output negative, he must put first the machine with the funcion y = sqrt(x-5)

Suppose you use initial value x = 9

Then the first machine will transform it to sqrt (9-5)  = sqrt(4) = 2 and the second machine y = 2^2 -6 = 4 - 6 = -2.